CHINA Mathematical Olympiad-1998 | SCHOOL OF OLYMPIAD | Quadratic | (L-1)

We have to simplify an expression and calculate it without actually calculating.

School of OLYMPIAD is a brand new series by MAX MATH GAMES where we will be solving many questions were asked in Junior Maths Olympiads.

This one is from CHINA 1998 Junior Maths Olympiad (China Mathematical Competitions for Secondary Schools except for CHNMOL)

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[lololol]

At the end, suppose the test forbids the use of calculators, how are we supposed to calculate 1998² ? Any tricks?

[serhiypidkuyko]

it's a simple question:
let x = 1999
then the expression = (1/2)√[(x-1)x(x+1)(x+2)+1] = (1/2)(x^2+x-1) = (1/2)(1999^2+1998)
since (x-1)x(x+1)(x+2)+1 = (x^2+x)(x^2+x-2)+1=(x^2+x)^2 - 2(x^2+x) + 1 = (x^2+x-1)^2

[matheusurbano]

Consider solving some OBM questions. This one is the brazilian mathematics olympiad